42482 Atul Bhalla et al./ Elixir Nuclear & Radiation Phys. 98 (2016) 42482-42485 Available online at www.elixirpublishers.com (Elixir International Journal) Nuclear and Radiation Physics Elixir Nuclear & Radiation Phys. 98 (2016) 42482-42485 Investigations on Nuclear Counting System using Data Acceptance Tests Atul Bhalla1,2*, Heena Duggal1, Navjeet Sharma2, J.S. Shahi1 and D. Mehta1 1Department of Physics, Panjab University, Chandigarh-160014, India. 2Department of Physics, D.A.V. College, Jalandhar-144004, India. ARTICLE INFO ABSTRACT Article history: This investigation uses Multi Channel Analyser (MCA) coupled with Received: 30 July 2016; Gamma Ray Spectroscope (GRS) to investigate some common counting 1 3 7 Received in revised form: statistics used for radiation measurements of a Cs gamma source. 26 August 2016; Few statistical tests involving 25 and 100 trials for data acceptance Accepted: 5 September 2016; were applied to study the stability of counting system. The statistical analysis evaluated count data on on four primary criteria; the Ratio Keywords Test, Chauvenet’s Criterion, the Chi-square test, and a control chart. Multi Channel Analyser, The control chart also reflected almost accurate statistical data except Gamma Ray for a minor error during few points of the 25 trial test. Fano factor was Spectroscope, also evaluated for both trials to ascertain the measure of reliability and Poisson distribution. signal to noise ratio of the equipment. The results demonstrated that the counting system was fairly accurate, with a few exceptions. The Ratio Test, Chauvenet’s Criterion, and the Chi-square test each, was passed successfully. After evaluating the statistical data, Poisson distribution was created to better analyze the data. © 2016 Elixir All rights reserved. Introduction large deviations. Poisson or Gaussian (Normal) distribution Any scientific experiment, including radioactivity, is can be utilized to understand the statistical models followed by generally subjected to an error in measurement. Primarily two the observed inherent fluctuations. This framework plays an types of error exists for raw data; determinate (or systematic) important role in ascertaining the effectiveness of and indeterminate (or random). The determinate errors measurement equipment and procedures, and to know if data includes the correctable factors such as the dead time of belong to the same random distribution [3]. detector, impact of background counts or due to improper Theoretical Background shielding of detector etc. whereas random errors cannot be The present investigations were undertaken to evaluate eliminated as they may be arising from fluctuations in testing the usefulness and accuracy of raw collected data by using and measurement conditions and can be evaluated by data acceptance tests namely, T-ratio test, Chauvenet’s statistical methods. In general, the reproducibility of data is a Criterion, Chi-square test, control chart test and Fano factor vital aspect but not in case of stochastically random processes analysis, each relying on different data information. The T- of radioactivity[1].Within any given time interval the emitted test, also called the ratio test, verifies the probability of radiation are subjected to unavoidable statistical fluctuations occurrence of any two consecutive values. It is a rapid method and different counts are observed in iteration as decay to identify background noise affecting data collection in the probability of each decaying atom is different. The statistical counting system. Since the ratio test requires only two data analysis makes it possible to ascertain the probability of count points, so it can be implemented on initial observations in an rate within certain limits of the true or average count rate. The investigation to fix any measurement errors [1]. Using the first nuclear counting statistics involves the framework to process two points x1 the raw data and predict about the expected precision of and x2,where derived quantities. The comparison of observed fluctuation (1) with predicted result from statistical models can tell about existing abnormality in the counting system. A trial or the number of decays in a given interval is independent of all and if T > 3.5, then, there is less than a 1 in 2000 chance that previous measurements, due to randomness of the undergoing the observed data is statistically accurate and this processes [2]. For a large data, the dispersion or deviation measurements should be rejected and the counting system from the mean count rate adapts in a predictable distribution. must be recalibrated before taking fresh observations. The shape of probability distribution function specifies the The Chauvenet’s Criterion is used to reject statistically extent of internal fluctuations in the data set. The width of the “bad data” or “wild points”. This test identifies significant curve about its mean value gives the relative measure of outliers that skew the data towards one direction so they can existing dispersion or scatter. For finite data the experimental be discarded from the set of observations due to large mean value can be regarded true mean value and small deviations from the calculated mean [4]. For relatively small deviations from the mean value are much more likely than Tele: +91 181-2203120 E-mail address: [email protected] © 2016 Elixir All rights reserved 42483 Atul Bhalla et al./ Elixir Nuclear & Radiation Phys. 98 (2016) 42482-42485 set of counts, outlier points can significantly change the mean produced from the excited crystal. The intensity of photon so and standard deviation [1]. emitted, is dependent on the energy of the exciting radiation. th If xi and xm are i trial and mean value respectively, then These photons strike the photocathode located at the end of (2) the photomultiplier (PMT) tube and eject photo-electrons by undergoing the photoelectric effect. The high voltage is applied from the power supply to maintain a large potential The standard table values helps in identifying any difference between the two ends of the PMT. Several significant deviations from the expected values then rejecting electrodes, called as dynodes, are arranged along the length of them according to Chauvenet’s Criterion [5]. the tube with increasing potential. As these electrons travel The next assessment for goodness of fit is obtained by the down the tube, they gain energy and get accelerated, then on Chi-square test to find out whether the observed data is part of striking another dynode releases furthermore electrons. These the same or any other random distribution [6]. electrons are multiplied as they travel through a series of The Chi-square value is given by dynode layers. This causes an avalanche or cascade of ejected χ2 = (3) electrons, and finally an output electrical pulse is obtained at end of the photomultiplier tube. The output is a resulting The χ2 values can be calculated for the entire data set and slightly amplifed pulse, which is then fed into a preamplifer, compared to the values in standard table using the value of where the signal is inverted and then fed to the amplifer. statistical degrees of freedom as f = N-1 to find the probability Typical gains of such dynode chains ranges from several function P (χ2) where N is the number of measurement s the thousand to one million and in the present setup coarse gain of experimental mean has been obtained from the same data [7]. 1K was used. This electrical pulse passes through a In case of large samples, for a perfectly fit to the Poisson preamplifer and then in an amplifer for further amplification distribution the χ2 value is 0.50. The malfunction of setup is of the signal. This signal is then passed through a indicated by very large fluctuations in the data set. When 0.01 discriminator, which rejected all pulses below a certain < P (χ2) < 0.90, the data is considered acceptable. When 0.05 threshold voltage. Finally, the resulting signal is fed to the < P (χ2) < 0.10 data is considered marginal and finally, when counter which records the number of pulses received in 0.90 < P (χ2) < 0.95, then data should be rejected [8]. tunable time intervals. The signal gain, the distance between source and detectors etc, are so adjusted that nearly mean The control chart evaluations are to ascertain that -1 dispersion in the data points. If points are too scattered then count rates of 8.36 and 351.8 sec (Hz) are obtained. The the experimental mean is not a true or faithful or effective numbers of counts were recorded for fixed time interval of 10 representation of the entire data set. The acceptability of data second for each trial of 25 and 100 data points respectively. can be ensured with its help. The smaller value of the standard The numbers of counts over a period of 100 seconds for each deviation (SD = σ) implies the greater the reproducibility of of these mean count rates were also recorded to ascertain the measurement. In the control test, each data point is classified range of mean count rate. The schematics of system setup are according to its location away from the mean line in terms of illustrated in Fig.1. In this study, Multi-Channel Analyzer (8K the number of standard deviations σ. If one data point exceeds MCA, Type MC 1000U, Make: Nucleonix, Hyderabad) was the limit of ±3σ, then the measurement must be repeated as it used which took several hundred channels counts has crossed the control limit (CL). If 2 any out of 3 simultaneously while retaining a low dead time, creating a consecutive data points are outside the limit of ±2σ then the more reliable and accurate spectrum. The PHAST MCA measurement must be repeated and is referred as Warning software was used for this study as default spectroscopy Limit (WL). If any 4 data points exceed consecutively the software, along with the other compatible equipments were limit of ±σ, then add another measurement in the counts.